Percentage Calculator
Calculate percentages, changes, and ratios with ease.
How to Calculate Percentages
Percentages are a way to express a number as a fraction of 100. The word "percent" comes from the Latin "per centum," meaning "by the hundred." Understanding percentages is essential for everyday tasks like calculating tips, discounts, taxes, and interest.
Basic Percentage Formulas
- Find X% of Y: Result = (X ÷ 100) × Y
- X is what % of Y: Percentage = (X ÷ Y) × 100
- Percentage change: Change = ((New − Old) ÷ Old) × 100
A useful mental shortcut: to find 10% of any number, move the decimal point one place to the left. To find 1%, move it two places. From there you can build any percentage — 15% is 10% plus half of 10%, and 5% is half of 10%. With a little practice, you can estimate most everyday percentages without reaching for a calculator.
Common Percentage Uses
- Shopping: Calculate discounts, sales tax, and price comparisons.
- Tipping: Calculate 15%, 18%, or 20% tip at restaurants.
- Finance: Interest rates, investment returns, and loan costs.
- Statistics: Express data as proportions of a total.
- Business: Profit margins, growth rates, and market share.
Percentage Examples
To find 15% of 200: (15 ÷ 100) × 200 = 30. To find what percent 30 is of 150: (30 ÷ 150) × 100 = 20%. To calculate the percentage change from 100 to 125: ((125 − 100) ÷ 100) × 100 = 25% increase.
Here are a few more worked examples that come up often. A $60 shirt marked 30% off saves you $18 and costs $42 — calculated as 60 × 0.30 = 18, then 60 − 18 = 42. If your investment grows from $5,000 to $6,200, the return is ((6,200 − 5,000) ÷ 5,000) × 100 = 24%. If a city's population rises from 80,000 to 84,000, the growth is ((84,000 − 80,000) ÷ 80,000) × 100 = 5%.
Percentage Increase vs. Percentage Decrease
The change formula works in both directions. A positive result is an increase and a negative result is a decrease, but the magnitude is what matters. For example, if a stock falls from $80 to $60, the change is ((60 − 80) ÷ 80) × 100 = −25%, meaning a 25% decrease. Notice that the same dollar move in reverse — from $60 back to $80 — is a 33% increase, not 25%. This asymmetry is why percentage change can be misleading when comparing up and down moves of the same size.
Percentage Points vs. Percent Change
A common source of confusion is the difference between "percentage points" and "percent change." If an interest rate rises from 4% to 5%, that is a 1 percentage point increase, but it is a 25% increase in the rate itself (because 1 ÷ 4 = 0.25). News headlines about tax rates, unemployment, and poll results usually refer to percentage points, while finance and science reports usually refer to percent change. Knowing which one you're reading prevents costly misunderstandings.
Working Backwards: Finding the Original Value
Sometimes you know a percentage and the result, but not the original number. If a price after 20% tax is $120, the original price is 120 ÷ 1.20 = $100. If a test score of 45 represents 75% of the total, the total is 45 ÷ 0.75 = 60. The general rule: divide the known result by (1 + rate) when the percentage was added, or by the rate itself when you're converting a part back to a whole.
Compound Percentage Changes
When percentages apply one after another, they compound rather than add. A 10% raise followed by another 10% raise is not a 20% raise — it's 1.10 × 1.10 = 1.21, or 21% total. The same logic applies to discounts: 20% off then another 20% off leaves you paying 0.80 × 0.80 = 0.64, or 64% of the original price — a 36% total discount, not 40%. This matters when comparing multi-step promotions or multi-year growth rates.
Practical Tips for Working with Percentages
- Always confirm which number is the base (the "of" value) before dividing — mixing up part and whole is the most common percentage mistake.
- When comparing two periods, use the earlier value as the base unless you have a reason not to.
- Round only at the end of a calculation to avoid compounding rounding errors.
- Watch for percentages above 100% — they're valid and common when measuring growth from a small base.
- Remember that a 50% increase followed by a 50% decrease does not return you to the starting value — you end up at 75% of it.
Frequently Asked Questions
To calculate X% of a number Y, multiply Y by X divided by 100. For example, 20% of 50 = (20 ÷ 100) × 50 = 10.
Subtract the original value from the new value, divide by the original value, then multiply by 100. If the result is positive, it's an increase; if negative, it's a decrease.
A percentage is a proportion out of 100. A percentile is a statistical measure indicating the value below which a given percentage of data falls. They are different concepts despite similar names.